7.4 Suppose that the hourly output of chili at a barbecue (q, measured in pounds) is characterized by where K is the number of large pots used each hour and L is the number of worker hours employed.

a. Graph the q=2,000 pounds per hour isoquant.

b. The point K=100, L=100 is one point on the q=2,000 isoquant. What value of K corresponds to L=101 on that isoquant? What is the approximate value for the RTS at K=100, L=100?

c. The point K=25, L=400 also lies on the q=2,000 isoquant. If L=401, what must K be for this input combination to lie on the q=2,000 isoquant? What is the approximate value of the RTS at K=25, L=400?

d. For this production function, the RTS is RTS=K/L. Compare the results from applying this formula to those you calculated in part b and part c. To convince yourself further, perform a similar calculation for the point K=200, L=50.

20q KL

7.7 The production function where , is called a Cobb-Douglas production function. This function is widely used in economic research. Using the function, show that

a. The chili production in problem 7.4 is a special case of the Cobb-Douglas.

b. If , a doubling of K and L will double q.

c. If , a doubling of K and L will less than double q.

d. If , a doubling of K and L will more than double q.

e. Using the results from part b through part d, what can you say about the returns to scale exhibited by the Cobb-Douglas function?

0 , 1a b

1a b

a bq K L

1a b

1a b